….Formal education in science and engineering centers on teaching facts and problem-solving skills in a series of narrow topics. It is true that a few topics, although narrow in content, have such broad application that they are themselves integrative: These include (at a bare minimum) substantial chunks of mathematics and the basics of classical mechanics and electromagnetism, with the basics of thermodynamics and quantum mechanics close behind.….To avoid blunders and absurdities, to recognize cross-disciplinary opportunities, and to make sense of new ideas, requires knowledge of at least the outlines of every field that might be relevant to the topics of interest. By knowing the outlines of a field, I mean knowing the answers, to some reasonable approximation, to questions like these:

What are the physical phenomena?What are their magnitudes?What are their preconditions?How well are they understood?How well can they be modeled?What do they make possible?What do they forbid?

And even more fundamental than these are questions of knowledge about knowledge:

What is known today?What are the gaps in what I know?When would I need to know more to solve a problem?How could I find it?

It takes far less knowledge to recognize a problem than to solve it, yet in key respects, that bit of knowledge is more important: With recognition, a problem may be avoided, or solved, or an idea abandoned. Without recognition, a hidden problem may invalidate the labor of an hour, or a lifetime. Lack of a little knowledge can be a dangerous thing.

Herrnstein and his coworkers devised a very advanced set of materials geared to teaching seventh-graders fundamental concepts of problem solving that were not targeted to any particular subject matter. In effect they, they tried to make the children smarter by giving them handy implements for their intellectual tool kits.

What were those non-subject specific, cognitive skills?

Basics of Classification

Hypothesis Testing

Discovery of Properties of Ordered Dimensions

Analogies

Simple Propositions

Principles of Logic

Constructing and Evaluating Complex Arguments

Weighing opportunity costs vs. probability of success for a goal

Evaluating credibility and relevance of data

I would have added metaphors, pattern-recognition and intuitive thinking games but it was a fine set of skills and the results were remarkable, according to Nisbett:

The instruction resulted in big changes in children’s ability to solve problems that the new skills were designed to improve….for language comprehension, .62 SD [ standard deviation]; for learning how to represent ‘”problem spaces,” .46 SD; for decision making, .77 SD; for inventive thinking, .50 SD. In short, general problem solving skills can be taught, and taught moreover in a brief period of time.

In psychometric terms, for a 13 year old, these scores represent phenomenal improvements in cognitive performance and indicate the plasticity of some aspects of measured intelligence.

We need to think of lessons and learning not just in terms of content or broad “critical thinking” but also the very specific cognitive actions that we want the students to experience – and the students need to have opportunities to use them across all subjects.